{
  "id": "1407.8299",
  "version": "v1",
  "published": "2014-07-31T07:24:34.000Z",
  "updated": "2014-07-31T07:24:34.000Z",
  "title": "Microlocal properties of scattering matrices",
  "authors": [
    "Shu Nakamura"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider scattering theory for a pair of operators $H_0$ and $H=H_0+V$ on $L^2(M,m)$, where $M$ is a Riemannian manifold, $H_0$ is a multiplication operator on $M$ and $V$ is a pseudodifferential operator of order $-\\mu$, $\\mu>1$. We show that a time-dependent scattering theory can be constructed, and the scattering matrix is a pseudodifferential operator on each energy surface. Moreover, the principal symbol of the scattering matrix is given by a Born approximation type function. The main motivation of the study comes from applications to discrete Schr\\\"odigner operators, but it also applies to various differential operators with constant coefficients and short-range perturbations on Euclidean spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-31T07:24:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58J50",
      "35P25",
      "81U05"
    ],
    "keywords": [
      "microlocal properties",
      "scattering matrices",
      "pseudodifferential operator",
      "born approximation type function",
      "scattering matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.8299N"
    }
  }
}